The hyperbolic cosecant is defined as csch z congruent 1/(sinh z) = 2/(e^z - e^(-z)). It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent though csch z = coth(1/2 z) - coth z. The derivative is given by d/(d z) csch z = - coth z csch z, where coth z is the hyperbolic cotangent, and the indefinite integral by integral csch z d z = ln[sinh(1/2 z)] - ln[cosh(1/2 z)] + C, where C is a constant of integration.

Bernoulli number | bipolar coordinates | bipolar cylindrical coordinates | cosecant | Helmholtz differential equation--toroidal coordinates | hyperbolic functions | hyperbolic sine | inverse hyperbolic cosecant | Poinsot's spirals | surface of revolution | toroidal function